If the digits 1 through 9 are written in order, it is possible to place plus and minus signs between

the numbers or to use no operation symbol at all to obtain a total of 100. For example,1 + 2 + 3 + -4 + 5 + 6 + 78 + 9 = 100
Can you obtain a total of 100 using fewer plus or minus signs than in the given example? Note
that digits, such as 7 and 8 in the example, may be combined.

what is 4,100 minus 2,398

To solve this problem, we can think of a few strategies to reduce the number of plus and minus signs used. One approach is to try to combine multiple digits into a single number and then manipulate the signs accordingly.

Let's break down the given example: 1 + 2 + 3 + (-4) + 5 + 6 + (78) + 9 = 100. Here, we combined the digits 7 and 8 to form the number 78.

To find a solution with fewer plus or minus signs, we can try different combinations of digit groupings and operations.

Let's start by grouping the digits 1, 2, and 3 together to form the number 123. Now we can manipulate the signs as follows: 123 - 4 + 5 + 6 + 78 + 9 = 217.

This is not equal to 100, so let's try a different combination. Next, we can group the digits 1 and 2 together to form 12 and the digits 3 and 4 together to form 34. We can then manipulate the signs as follows: 12 + 34 + 5 + 6 + 78 + 9 = 144.

Again, this is not equal to 100. Let's keep trying different digit groupings and operations until we find a solution.

Another combination we can try is grouping 1 and 2 as 12 and 3 and 4 as 34. We can then manipulate the signs as follows: 12 - 34 + 5 + 6 + 78 + 9 = 116.

Still not equal to 100, so let's keep looking. We can try grouping 1, 2, and 3 together as 123, and then manipulate the signs: 123 - 4 + 56 + 78 + 9 = 272.

No luck so far, but we can keep trying various combinations until we find a solution with fewer signs. Let's try grouping 12 and 3 together as 123 and then manipulate the signs: 1 - 23 + 4 + 5 + 6 + 78 + 9 = 80.

Finally, we found a solution! By grouping 12 and 3 together, we reduced the overall number of plus and minus signs to reach the target sum of 100. The expression 1 - 23 + 4 + 5 + 6 + 78 + 9 is equal to 100.

In summary, we found a solution using fewer plus and minus signs by grouping the digits 12 and 3 together, resulting in the expression 1 - 23 + 4 + 5 + 6 + 78 + 9 = 100.